Game Theory: A Very Short Introduction

Within the framework of the "a very short introduction" written as a qualitative and popular work rather than a formal text or a text for a specific audience Ken Binmore turned out an excellent qualitative survey of game theory. Binmore presents a history of the people that formulated game theory, an overview of the mathmatical models and processes, and a superb discussion of the applications of the various tools. If you're looking for derivations, sigma notation, and other mathmatica that make this liberal arts major's head spin, you might consider Games and Decisions: Introduction and Critical Survey. Unlike other books on game theory, Binmore pays considerable attention to the psychology of the actors in games and how that impacts their decision processes and the value of strategy availible to an opposing player. E. M. Van Court

*Brilliant, brilliant! This is a marvellous book in a series which is fairly uneven and appears to have little editorial oversight, but the author has no need of an editor. Binmore is famous for being an outstanding teacher, a great textbook writer, a prolific researcher, and a strong controversialist. The book is balanced, clear, and well-written, and has an excellent bibliography. It is entirely reliable: the reader has to take Binmore's word on technical points now and again, especially towards the end (to take just one instance, convexity of the bargaining set with two risk-averse players) but one can depend on him absolutely. The exposition is a model of simplicity and compression: the account of von Neumann-Morgenstern utility exceeds all previous simplifications, including his own; and the avoidance of calculus everywhere, especially in the Nash bargaining solution, is almost magical. I noticed two blatant typographic errors and one unlabelled axis: no doubt the publisher's, Oxford's, fault. The thing could not have been done better, and nobody but Binmore could have done it. *Brilliant, brilliant! *(to quote an excited Tony Cosier commenting on an outfield catch by Mike Brearley of Andy Roberts off Mike Hendrick in the cricket World Cup Final at Lord's in June 1979).

This is a frustrating book to review because it so variable. Clearly Ken Binmore knows much about his subject and there are moments when the book comes alive with insights and crystal clear explanations. You want to cheer. By the time I had finished I knew a lot more about Game Theory than when I started, as is the case with most titles in this excellent series from Oxford. But then you continually hit rather over condensed technical explanations which clearly mean a lot to Ken Binmore, but leave the general reader floundering. He finds it difficult I suspect to put himself in the other's shoes and his editor did not push him hard enough to be clear.The book would benefit from either a technical glossary of key terms used or concise and clear boxed definitions in the text of, for example, Nash Equilibrium. There is not a lot of doubt in this book, which sometimes comes over as arrogant. His dismissal of probably the most useful (to a professional negotiator like myself) book on bargaining 'Getting to Yes' is telling: 'This best seller argues that good bargaining consists of insisting on a fair deal. Thinking strategically is dismissed as a dirty trick!'This misses the fundamental point of Getting to Yes: Interest based bargaining and expanding the size of the pie to be divided creatively. I hope his dismissal of others he disagrees with (and with whom I am less familiar) is more balanced and realistic. Yet there is clearly a very interesting, well informed, intelligent Ken Binmore there to be had, but not consistently. His short explanations of evolutionary game theory and reciprocity are exemplary. And this book made me want to read some of his other work, to see if he is more balanced when he has more space. When he is not being flip his bibliography is outstanding. On balance I would still say: read it!